Option B: 300 m
Using $\sin 30° = \dfrac{\text{height}}{\text{string length}}$, we get $\dfrac{1}{2} = \dfrac{150}{L}$, so $L = 300$ m.
The height (150 m) is the side opposite the 30° angle, and the string is the hypotenuse. Use $\sin\theta = \text{opposite}/\text{hypotenuse}$. $\sin 30° = \frac{1}{2}$, giving $L = 150 \times 2 = 300$ m. Don't confuse with $\tan$ or $\cos$ here.